First character death. How did you handle it?
I really don't have any clear recollection of the first character death in a game I ran. I think the victim was a thief, but beyond that I can't say. I don't recall how it happened, whether it was a monster or a trap, or any other circumstances surrounding it. That in itself is a pretty strong indication of how we handled it: We moved on quickly. Yes, it sucks to lose a character, but you make a new one. I don't remember my game being of particularly high lethality; character death wasn't a regular occurrence, but it did happen now and then. It was just part of the game.
Really, I think one of the "jump the shark" moments for that first campaign came when we got the Expert Set and learned of the raise dead spell. After that, no character who died ever stayed dead. I think I initially set the price to have a dead character raised at a temple at 1,000 gp and eventually bumped it to 5,000, which stung the players a little bit, but not sufficiently that they'd leave a PC in the grave.
I actually do have an account of the first time a character of my own bit it, too, and incidentally a related big-monster-slaying story that somehow got misplaced in my brain when I wrote the post for day 4.
I was in a group that played 2E for a while, and rolled up a halfling thief by the name of Emory Bramblethorn for a one-shot run through part of the Against the Giants series. He had just scrambled up a tower wall and through a window of a giant keep, as part of some advance scouting and hopefully looting, and found a giant there. My intrepid burglar quickly hid before the none-too-vigilant giant spotted him, and when the giant turned and headed down the stairs, it was backstabbing time! I had in mind to wait until the giant was down the stairs enough to put his back at halfling-sword level, do whatever damage I could by surprise, and then skitter away before he could make a halfling pancake. I rolled - a 20! Shortsword, that's 1d8 vs. large creatures in 2E - max damage! Doubled for the natural 20, quadrupled for backstab, 64 points of damage, and down went the giant! After recovering from being completely dumbfounded at his success, Emory trotted down the stairs, opened the gate for the others, and nonchalantly said, "There was one up there, but don't worry. I got him."
Sadly, Emory met his end a short time later while trying to stay out of the way in a toe-to-toe fight between the party and some other giants. It was quite the anticlimax after his crowning moment of awesome with the sentry in the tower.